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UNIT 2
: SYSTEMS OF EQUATIONS
LESSON 1 : COORDINATE GEOMETRY
The Cartesian Plane
Consider the grid
below. The center of the grid is called
the origin (Point O). The horizontal number line is called the
x-axis.
The vertical number line is
called the y-axis. Any point in the x-y plane may be located with
reference to the origin using two numbers,
called an ordered pair of numbers (x,y). Complete the chart and graph below (Example
1)to see how this is done.
Example 1:
|
POINT |
LOCATION FROM ORIGIN IN WORDS |
ORDERED PAIR (x,y) |
|
A |
right 1, up 2 |
A(1,2) |
|
B |
left 3, up 4 |
B(-3,4) |
|
C |
right 5, down 2 |
C(5,-2) |
|
D |
|
D( , ) |
|
E |
|
E( , ) |
|
F |
|
F( , ) |
|
G |
|
G( , ) |
|
H |
|
H( , ) |
|
I |
|
I( , ) |
|
J |
|
J( , ) |
|
K |
|
K( , ) |
|
L |
|
L( , ) |
Solution:
|
POINT |
LOCATION FROM ORIGIN IN WORDS |
ORDERED PAIR (x,y) |
|
A |
right 1, up 2 |
A(1, 2) |
|
B |
left 3, up 4 |
B(-3, 4) |
|
C |
right 5, down 2 |
C(5, -2) |
|
D |
left 2 down 4 |
D(-2, -4) |
|
E |
right 1, down 3 |
E(1, -3) |
|
F |
left 5, down 5 |
F(-5, -5) |
|
G |
right 6 up 1 |
G(6, 1) |
|
H |
left 5, up 7 |
H(-5, 7) |
|
I |
right 4, no up 0 |
I(4, 0) |
|
J |
left 6, up 0 |
J( 6, 0) |
|
K |
right 0, up 3 |
K(0, 3) |
|
L |
right 0, down 1 |
L(0,-1) |
Terminology:
The elements of column 3 are
called ordered pairs. Each ordered pair has an x-coordinate and a
y-coordinate (x , y).
The horizontal number line
is called the x-axis.
The vertical number line is the y-axis. The
origin has coordinates (0 , 0).
Graphing Regions in The Cartesian Plane
Example 2:
Sketch
and describe the regions given by the following set descriptions.
a) This region is all the points in the plane on the vertical line x = -2 or to the right of it. See graph below
b) This region is all the points in the plane on the horizontal line y = 3 or below it. See graph below
c) This region is all the points in the plane to the right of the line x = -1, but not including the line, and to the left of the line x = 2, including the
points on the line. The line x = -1 is dashed to show the points on the line are not included.
a)
Distance Between Two Points (length of a
line segment)
